Givi Berikelashvili

Convergence of Fourth Order Compact Difference Schemes for Three-Dimensional Convection-Diffusion Equations

We consider a Dirichlet boundary-value problem for the three-dimensional convection-diffusion equations with constant coefficients in the unit cube. A high order compact finite difference scheme is constructed on a 19-point stencil using the Steklov averaging operators. We prove that the finite difference scheme converges in discrete

A one-parameter family of difference schemes for the regularized long-wave equation

W_2^m(\omega)

Method of corrections by higher order differences for elliptic equations with variable coefficients

-norm with the convergence rate

On the improvement of convergence rate of difference schemes with high order differences for a convection-diffusion equation

O(h^{s-m})

High Order Difference Scheme for Helmholtz Equation with Mixed Boundary Conditions

, where the real parameter

On a numerical solution of one nonlocal boundary-value problem with mixed Dirichlet–Neumann conditions

s

On the convergence of difference schemes for one nonlocal boundary-value problem

satisfies the condition

On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation

\max (1.5, m)<s \le m+4

Method of Refinement by Higher Order Differences for 3D Poisson Equation with Nonlocal Boundary Conditions

,

Method of corrections by higher order differences for one nonlocal boundary-value problem

m=0,1,2